[sdiy] Walsh Functions/EN S-008

Fri Sep 15 23:52:54 CEST 2017

Tom --

Thanks for the discussion.  I can tell from your response that I haven't 
explained myself well enough. Here goes for another try.

Multiple pulsed or stepped waveforms have different spectra and sounds 
from traditional waveforms.  (If you are happy with the MacMoog 
waveforms, then fine.) The new spectral features extend throughout the 
audio range.  The ones at the lower end give timbers that are 
fundamentally different from traditional ones.  The ones at high 
frequencies are strong, sure.  But ultimately they roll off at 6 dB / 
Oct, just like the traditional Saw and Pulse waveforms.  Obviously, you 
can use LP filtering to reduce the brightness, just as you might on the 
traditional waveforms. For some analytics on typical double-pulse 
waveforms, please refer to Bernie's EN #228, available online:
http://electronotes.netfirms.com/free.htm

 >>>
What’s wrong with trying to transform a flute into a clarinet? One has 
hardly any harmonics, and the other has a few more, but neither have 
many. If you don’t like that example, pick one with less. It doesn’t 
matter. The point is only: why limit yourself to waveforms with a lot of 
harmonic content? Why is that better?
<<<

I think you may have  misunderstood what I was trying to say.  I asked 
why you would use a Walsh generator to morph between low harmonic 
content waveforms, when there are simpler methods available.  What 
simple methods, you ask? Well, dynamic mixing of the two waves is 
probably the easiest method, at least conceptually.  For your 
flute-clarinet question, you can  morph between Tri and Square waves by 
amplifying and clipping the Tri.  Morphing Tri to Saw is a bit trickier, 
but a few years back I figured out how to do this using a saturating 
negative impedance converter. A fairly detailed explanation, with 
representative sound clips, is on my website:
http://ijfritz.byethost4.com/sy_cir10.htm
I actually have dedicated versions of this circuit on two of my VCOs. 
The advantage of morphing vs mixing is there are no steps, so driving 
other waveshapers goes more smoothly.

 >>>
The more interesting stuff for me is the subtler changes in timbre that 
can be achieved, that give the ear interest but don’t “wow!” it with 
unusual gimmicks.
<<<

Actually, with a greater variety of waveform choices you have WAY MORE 
scope along these lines.  I did a lot of work years ago synthesizing 
quasi-realistic sounds.  I've never put all this up, but short 
representative clips are here:
http://ijfritz.byethost4.com/sy_close.htm
Almost all these sounds were generated using the Double Pulse Waveform 
Generator or the DoubleDeka 10-step VCO.  (At least if "the high quickly 
wears off and these are sounds that get tired fast", the clips are short.)

There are many examples of sounds from pulse/step waveform sources on my 
website and you tube channel.
http://ijfritz.byethost4.com/  website index
  http://ijfritz.byethost4.com/sy_cir8.htm  5 Pulser Waveshaper Project
http://ijfritz.byethost4.com/sy_cir5.htm  Double Pulse Waveform generator
http://ijfritz.byethost4.com/sy_cir6.htm   Wavolver
http://ijfritz.byethost4.com/sy_cir10.htm  SNICster
http://ijfritz.byethost4.com/MiscProj/DD.htm  DoubleDeka
https://www.youtube.com/user/frijitz001  Demos of commercialized modules

There are also numerous comments and videos from other users of these 
modules on the electro-music and muff's forums and on you tube.  This 
post is already too long, so I won't elaborate on all these.

 >>>
For this reason I’ve been looking at the way shifting the phase of the 
harmonics in a waveform affects the crossfade between one waveform and 
another - suddenly something that was previously a simple linear 
crossfade becomes non-linear and more interesting, not in a ‘grab you by 
the ears and shake you” way but rather something more subtle. This for 
me is more where I’d like to be.
<<<

I have no idea what this means.  But by all means, please get back to us 
when you actually have something to show.

Ian

On 9/14/2017 5:45 PM, Tom Wiltshire wrote:
> Hi Ian,
> 
> Thanks for that report. It’s very interesting. “Smooth, even if fairly extreme” is something I might need to hear to understand. Yes, I understand that there will be a fairly strong fundamental in any waveform like this - even if that’s mainly perceptual rather than actual. It’s still what we hear. Morphing between two low-harmonic waveforms has all kinds of uses. What’s wrong with trying to transform a flute into a clarinet? One has hardly any harmonics, and the other has a few more, but neither have many. If you don’t like that example, pick one with less. It doesn’t matter. The point is only: why limit yourself to waveforms with a lot of harmonic content? Why is that better?
> 
> I don’t understand what you mean by "why would you do it this way instead of by simple means?”. If it's important, please explain. I’m sorry I didn’t get it first time.
> 
> In many ways, I don’t think “extreme wave shaping” is my direction of travel. Extreme results are very quickly perceived as artificial, and in my view that makes them a “quick fix” - perhaps they’re exciting for a moment, but the high quickly wears off and these are sounds that get tired fast. The more interesting stuff for me is the subtler changes in timbre that can be achieved, that give the ear interest but don’t “wow!” it with unusual gimmicks. For this reason I’ve been looking at the way shifting the phase of the harmonics in a waveform affects the crossfade between one waveform and another - suddenly something that was previously a simple linear crossfade becomes non-linear and more interesting, not in a ‘grab you by the ears and shake you” way but rather something more subtle. This for me is more where I’d like to be.
> 
> Please understand I’m not trying to dissuade Pete or anyone else from doing their own experiments and coming to their own conclusions. One of the great things is that there’s a lot of different places to go and a lot of potential things to discover. It’d get dull fast if we all went in the same direction!
> 
> Regards,
> Tom
> 
>> On 14 Sep 2017, at 22:55, ijfritz at comcast.net wrote:
>>
>> Hmmm ... not sure about all that.  I have a VCO that has ten-step waveform generators.  I can make timbre changes by shoving the sliders around.  To my ear the changes sound smooth, even if fairly extreme.  Same thing with the extreme waveforms in my 5 Pulser waveshaper.  Remember, you almost always hear a strong fundamental frequency when doing this kind of morphing.  (Unless you deliberately suppress it.) But tell me, why would you want to morph between two low-harmonic content waveforms anyway?  I mean why would you do it this way instead of by simple means?
>>
>> I think it would be quite interesting to listen to dynamically changing Walsh-generated waveforms. There could well be interesting dynamic "phasy-ness".  Or interesting initial note transients. Or cool audio-frequency timbre modulation effects.
>>
>> Carry on Pete!  I've been working on extreme waveshaping for over thirty years, and several modules based on this work have been successfully commercialized.  I think you will almost certainly get some interesting results.  And of course it would be easy to generate these dynamic waveforms with simple code or simulations.
>>
>> Ian
>>
>>
>>
>>
>> Sent from XFINITY Connect Mobile App
>>
>>
>> ------ Original Message ------
>>
>> From: Tom Wiltshire
>> To: Pete Hartman
>> Cc: synth-diy at synth-diy.org DIY
>> Sent: September 14, 2017 at 5:02 AM
>> Subject: Re: [sdiy] Walsh Functions/EN S-008
>>
>> Isn’t the trouble with Walsh function synthesis that each coefficient controls a complex waveform with a whole fistful of harmonics? While it’s possible to carefully mix Walsh functions to get smooth-sounding waveforms by cancelling out higher harmonics, any minor tweak to the coefficient values is going to introduce large abrupt edges and significant high frequencies. That makes waveform morphing pretty much bound to go from A via buzziness to B.
>> Basing things on sine waves is so much simpler in many ways, despite Walsh functions being much easier to generate.
>>
>> Tom
>>
>> ==================
>>        Electric Druid
>> Synth & Stompbox DIY
>> ==================
>>
>>> On 14 Sep 2017, at 05:38, Pete Hartman <pete.hartman at gmail.com> wrote:
>>>
>>> There are a wide range of folks on here, including some who've been doing this stuff since ElectroNotes was young :) so I'm hoping maybe someone can help.
>>>
>>> I was perusing old issues, in particular #16, which came with a supplement S-008 on Walsh functions.  These functions were also discussed somewhat in #16 and a couple subsequent issues.  However I don't have a copy of S-008, and after asking Bernie about it, he has so far been unable to locate a copy.
>>>
>>> I suppose if I had my head more fully around the math of Fourier series it might not be so difficult for me, but I'm not grasping the entire idea of using the Walsh functions for waveform generation, and I'm kind of interested.  My thought is that while, as Bernie points out in #16 and his paper for AES, the generated waveforms themselves aren't particularly notable, modulating the coefficients of the different waveforms might sound different than other types of waveform modulation.  I'm interested to play around with it in any case.  Big picture wise, I see the parallel to Fourier and understand the concept, I'm just not following the nature of the coefficients to generate specific waveform types.
>>>
>>> I got the impression from the references to the supplement that it might help get me over the block I'm having.  But not having it myself, and so far unable to get one from the source (despite his much appreciated search for same) the question turns to whether any of y'all out there might have a copy of S-008?  If so, and if we can get Bernie's blessing (and probably send him a copy too), I'd be interested in some form of it that I could read.
>>>
>>> Thanks!
>>>
>>> Pete
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